A common way to demonstrate the existence of an EP in an experimental set-up is to follow a loop in parameter space and trace the eigenvalues accordingly. If the eigenvalues do not return to themselves, then there must be (at least one) EP structure inside the loop. Such an argument can already be found in [1]}, and in practice is done in a stroboscopic way by measuring the energy for sufficiently close discrete parameter values (e.g. in [2]}). The formal mathematics behind this argument is straightforward.
